908,145,623,777 ten-millions place of this number.

Start from the right-most 7, and go one digit to the left each time:
7 - units place
7 - tens place
7 - hundreds place
3 - thousands place
2 - ten-thousands place
6 - hundred-thousands place
5 - millions place
4 - ten-millions place    < answer to this question
1 - hundred-millions place
8 - billions place
0 - ten-billions place
9 - hundred billions place

The ten-millions place is the 4.